Method for manufacturing electronic apparatus

ABSTRACT

A method for manufacturing an electronic apparatus comprises forming a quartz crystal tuning fork resonator having a fundamental mode of vibration and a second overtone mode of vibration each comprised of a flexural mode of an inverse phase, a series resistance R 1  of the fundamental mode of vibration and a series resistance R 2  of the second overtone mode of vibration. An amplification circuit is provided having a CMOS inverter, a feedback resistor, a negative resistance −RL 1  for the fundamental mode of vibration of the quartz crystal tuning fork resonator, and a negative resistance −RL 2  for the second overtone mode of vibration thereof. A feedback circuit is provided having the quartz crystal tuning fork resonator, a plurality of capacitors and a drain resistor. The quartz crystal tuning fork resonator is electrically connected to the CMOS inverter and the feedback resistor of the amplification circuit and to the capacitors and the drain resistor of the feedback circuit.

CROSS REFERENCE TO RELATED APPLICATION

This Application is a division of copending U.S. patent application Ser. No. 10/412,470 filed Apr. 11, 2003 and claiming a priority date of Apr. 23, 2002.

FIELD OF THE INVENTION

The present invention relates to a quartz crystal resonator, a quartz crystal unit and a quartz crystal oscillator, and their manufacturing methods.

BACKGROUND INFORMATION

In general, a quartz crystal resonator is housed in a quartz crystal unit and a quartz crystal oscillator comprises the quartz crystal unit. For example, a quartz crystal oscillator with a quartz crystal unit comprising a contour mode resonator such as a quartz crystal tuning fork resonator, which is capable of vibrating in a flexural mode, is widely used as a time standard in consumer products, wearable time-keeping equipment and communication equipment (such as cellular phones, wristwatches and pagers). Recently, because of high frequency stability, miniaturization and the light weight nature of these products, the need for a smaller quartz crystal unit and a smaller quartz crystal oscillator with a smaller quartz crystal tuning fork resonator, capable of vibrating in a flexural mode and having a high frequency stability, a small series resistance and a high quality factor has arisen.

Heretofore, however, it has been impossible to obtain a quartz crystal unit and a quartz crystal oscillator because a conventional quartz crystal tuning fork resonator, capable of vibrating in a flexural mode can not be obtained with a high frequency stability, a small series resistance and a high quality factor when it is miniaturized.

Moreover, nothing teaches figure of merit M of the present invention which has an influence on a frequency stability for a flexural mode, quartz crystal tuning fork resonator capable of vibrating in a fundamental mode and teaches a relationship of an amplification circuit and a feedback circuit which construct a quartz crystal oscillating circuit of the present invention, and also, nothing teaches a method of manufacturing a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, a quartz crystal unit and a quartz crystal oscillator of the present invention.

Likewise, nothing teaches a method for manufacturing a quartz crystal unit comprising a contour mode resonator such as a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, and their resonators, according to the present invention.

In addition, for example, there been has a big problem in the conventional quartz crystal oscillator with the conventional quartz crystal tuning fork resonator, such that a fundamental mode vibration of the resonator jumps to a second overtone mode vibration by shock or vibration.

It is, therefore, a general object of the present invention to provide embodiments of a contour mode resonator such as a flexural mode, quartz crystal tuning fork resonator, a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, a quartz crystal unit with the contour mode resonator and a quartz crystal oscillator comprising a quartz crystal oscillating circuit with a flexural mode, quartz crystal tuning fork resonator, capable of vibrating in a fundamental mode, and having a high frequency stability, a small series resistance and a high quality factor, and also to provide embodiments of a method for manufacturing the contour mode resonator, the quartz crystal unit and the quartz crystal oscillator, which overcome or at least mitigate one or more of the above problems.

SUMMARY OF THE INVENTION

The present invention relates to a flexural mode, quartz crystal tuning fork resonator, capable of vibrating in a fundamental mode and having a nominal frequency of 32.768 kHz, a quartz crystal unit comprising a contour mode resonator such as a flexural mode, quartz crystal tuning fork resonator, a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, and a quartz crystal oscillator comprising a quartz crystal oscillating circuit having an amplification circuit and a feedback circuit, and also relates to their manufacturing methods.

It is an object of the present invention to provide a flexural mode, quartz crystal tuning fork resonator capable of vibrating in a fundamental mode and having a nominal frequency of 32.768 kHz.

It is an another object of the present invention to provide a quartz crystal unit comprising a contour mode quartz crystal resonator.

It is a further object of the present invention to provide a quartz crystal oscillator comprising a quartz crystal oscillating circuit with a flexural mode, quartz crystal tuning fork resonator, capable of vibrating in a fundamental mode, and having a nominal frequency of 32.768 kHz, a high frequency stability, a small series resistance R₁ and a high quality factor Q₁.

It is a still further object of the present invention to provide a method for manufacturing a plurality of individual quartz crystal tuning fork resonators capable of vibrating in a flexural mode, a quartz crystal unit comprising a contour mode quartz crystal resonator, a case and a lid, and a quartz crystal oscillator comprising: a quartz crystal oscillating circuit comprising; an amplification circuit comprising an amplifier at least and a feedback circuit comprising a flexural mode, quartz crystal tuning fork resonator and capacitors at least.

According to one aspect of the present invention, there is provided a method for manufacturing a plurality of individual quartz crystal tuning fork resonators each of which is capable of vibrating in a flexural mode, and each of the individual quartz crystal tuning fork resonators comprising the steps of: forming integrally tuning fork tines each of which has a length, a width and a thickness and the length greater than the width and the thickness, and a tuning fork base; providing grooves; and disposing electrodes inside the grooves and on sides of said tuning fork tines, and the grooves being provided at said tuning fork tines, and the electrodes being disposed opposite each other inside the grooves and on the sides of said tuning fork tines so that the electrodes disposed opposite each other are of opposite electrical polarity and said tuning fork tines are capable of vibrating in inverse phase, wherein the individual quartz crystal tuning fork resonators are provided in a quartz crystal wafer with resonance frequency higher than 32.768 kHz, each of which is capable of vibrating in a fundamental mode, and next, metal films are formed on said tuning fork tines in the quartz crystal wafer by a spattering method or an evaporation method so as to get the individual quartz crystal tuning fork resonators each of which has resonance frequency lower than 32.768 kHz, and wherein comprising the further steps of: adjusting the resonance frequency by removing a part or all of the metal films formed on said tuning fork tines in the quartz crystal wafer by laser trimming or a plasma etching method and inspecting the individual quartz crystal tuning fork resonators in the quartz crystal wafer, and when there is a failure resonator therein, it is removed from the quartz crystal wafer or something is marked on it or it is remembered by a computer.

According to a second aspect of the present invention, there is provided a method for manufacturing a quartz crystal unit comprising a contour mode quartz crystal resonator which is one of a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, a case and a lid, and said contour mode quartz crystal resonator comprising the step of: utilizing a particle method or a chemical etching method to form a resonator comprising; a vibrational portion; connecting portions located at ends of said vibrational portion; supporting portions connected to said vibrational portion through said connecting portions; and electrodes disposed opposite each other on upper and lower faces of said vibrational portion so that the electrodes disposed opposite each other are of opposite electrical polarity, wherein a plurality of individual contour mode quartz crystal resonators are formed in a quartz crystal wafer, each of which is capable of vibrating in a contour mode and a single mode, and wherein each of said individual contour mode quartz crystal resonators is mounted at a mounting portion of a case, and the resonance frequency of each resonator is adjusted by laser trimming or a plasma etching method so that a frequency deviation is within a range of −100 PPM to +100 PPM to a nominal frequency of less than 135 MHz when the quartz crystal unit is provided.

According to a third aspect of the present invention, there is provided a method for manufacturing a quartz crystal oscillator comprising: a quartz crystal oscillating circuit comprising; an amplification circuit comprising an amplifier at least and a feedback circuit comprising a quartz crystal tuning fork resonator and capacitors at least, said quartz crystal tuning fork resonator comprising the steps of: forming integrally tuning fork tines each of which has a length, a width and a thickness and the length greater than the width and the thickness, and a tuning fork base; providing grooves; and disposing electrodes inside the grooves and on sides of said tuning fork tines, and the grooves being provided at said tuning fork tines, and the electrodes being disposed opposite each other inside the grooves and on the sides of said tuning fork tines so that the electrodes disposed opposite each other are of opposite electrical polarity and said tuning fork tines are capable of vibrating in inverse phase, and said quartz crystal oscillating circuit comprising the step of connecting electrically said quartz crystal tuning fork resonator, the amplifier and the capacitors at least, wherein said quartz crystal tuning fork resonator is capable of vibrating in a flexural mode and said quartz crystal oscillating circuit comprises said quartz crystal tuning fork resonator whose figure of merit M₁ of a fundamental mode vibration is larger than figure of merit M₂ of a second overtone mode vibration to suppress the second overtone mode vibration and to get a high frequency stability for the fundamental mode vibration.

According to a fourth aspect of the present invention, there is provided a method for manufacturing a quartz crystal oscillator comprising: a quartz crystal oscillating circuit comprising; an amplification circuit comprising a CMOS inverter and a feedback resistor, and a feedback circuit comprising a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, resistors and capacitors, said quartz crystal tuning fork resonator comprising the step of: utilizing a chemical etching method to form a resonator comprising; tuning fork tines each of which has a length, a width and a thickness and the length greater than the width and the thickness, and a tuning fork base, and electrodes disposed on obverse and reverse faces and on sides of said tuning fork tines so that said tuning fork tines are capable of vibrating in inverse phase, said quartz crystal tuning fork resonator being formed in a quartz crystal wafer and a plurality of individual quartz crystal tuning fork resonators capable of vibrating each in a fundamental mode being formed therein, each of which comprises: tuning fork tines and a tuning fork base; and electrodes disposed on obverse and reverse faces and on sides of the tuning fork tines, and has resonance frequency higher than 32.768 kHz, wherein comprising the further steps of: forming metal films on the tuning fork tines of the individual quartz crystal tuning fork resonators in the quartz crystal wafer by a spattering method or an evaporation method so as to get the individual quartz crystal tuning fork resonators each of which has resonance frequency of 29.4 kHz to 32.75 kHz; mounting each resonator at a mounting portion of a case; and adjusting the resonance frequency of the each resonator by laser trimming or a plasma etching method so that it is within a range of 32.764 kHz to 32.772 kHz when a quartz crystal unit comprising said quartz crystal tuning fork resonator is provided, wherein said quartz crystal oscillating circuit comprising the amplification circuit and the feedback circuit is constructed so that a ratio of an absolute value of negative resistance, |−RL₁| of a fundamental mode vibration of the amplification circuit and series resistance R₁ of the fundamental mode vibration is larger than that of an absolute value of negative resistance, |−RL₂| of a second overtone mode vibration of the amplification circuit and series resistance R₂ of the second overtone mode vibration, and an output signal of said quartz crystal oscillating circuit is outputted through a buffer circuit and has a frequency of 32.764 kHz to 32.772 kHz, and wherein comprising the further step of inspecting the individual quartz crystal tuning fork resonators formed in the quartz crystal wafer, and when there is a failure resonator therein, it is removed from the quartz crystal wafer or something is marked on it or it is remembered by a computer.

The present invention will be more fully understood by referring to the following detailed specification and claims taken in connection with the appended drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 shows a general view of a flexural mode, quartz crystal tuning fork resonator embodying the present invention;

FIG. 2 shows a cross-sectional view of the tuning fork base along line 2-2 of FIG. 1 illustrating an electrode construction;

FIG. 3 shows a plan view of a quartz crystal tuning fork resonator of FIG. 1;

FIG. 4 shows a plan view of a flexural mode, quartz crystal tuning fork resonator embodying the present invention;

FIG. 5 a and FIG. 5 b show a plan view and a side view of a contour mode quartz crystal resonator capable of vibrating in a width-extensional mode embodying the present invention;

FIG. 6 shows a cross-sectional view of a quartz crystal unit embodying the present invention, and in which a quartz crystal tuning fork resonator is housed;

FIG. 7 shows a step diagram of a method for manufacturing a quartz crystal tuning fork resonator and a quartz crystal unit of the present invention;

FIG. 8 shows a diagram of an embodiment of a quartz crystal oscillating circuit which constructs a quartz crystal oscillator of the present invention;

FIG. 9 shows a diagram of the feedback circuit of FIG. 8;

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator embodying the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring now to the drawings, the embodiments of the present invention will be described in more detail.

FIG. 1 shows a general view of a flexural mode, quartz crystal tuning fork resonator 10 embodying the present invention and its coordinate system o-xyz. A cut angle θ, which has a typical value of 0° to 10°, is rotated from a Z-plate perpendicular to the z axis about the x axis. The quartz crystal resonator 10 comprises two tuning fork tines 20 and 26 and a tuning fork base 40. The tines 20 and 26 have grooves 21 and 27 respectively, with the grooves 21 and 27 extending into the base 40. In addition, the base 40 has the additional grooves 32 and 36.

FIG. 2 shows a cross-sectional view of the tuning fork base 40 for the quartz crystal resonator 10 along line 2-2 of FIG. 1. In FIG. 2, the shape of the electrode construction within the base 40 for the quartz crystal resonator of FIG. 1 is described in detail. The section of the base 40 which couples to the tine 20 has the grooves 21 and 22 cut into the obverse and reverse faces of the base 40. Also, the section of the base 40 which couples to the tine 26 has the grooves 27 and 28 cut into the obverse and reverse faces of the base 40. In addition to these grooves, the base 40 has the grooves 32 and 36 cut between the grooves 21 and 27, and also, the base 40 has the grooves 33 and 37 cut between the grooves 22 and 28.

Furthermore, the grooves 21 and 22 have the first electrodes 23 and 24 both of the same electrical polarity, the grooves 32 and 33 have the second electrodes 34 and 35 both of the same electrical polarity, the grooves 36 and 37 have the third electrodes 38 and 39 both of the same electrical polarity, the grooves 27 and 28 have the fourth electrodes 29 and 30 both of same electrical polarity and the sides of the base 40 have the fifth and sixth electrodes 25 and 31, each of opposite electrical polarity. In more detail, the fifth, fourth, and second electrodes 25, 29, 30, 34 and 35 have the same electrical polarity, while the first, sixth and third electrodes 23, 24, 31, 38 and 39 have the opposite electrical polarity to the others. Two electrode terminals E-E′ are constructed. That is, the electrodes disposed inside the grooves constructed opposite each other in the thickness (z axis) direction have the same electrical polarity. Also, the electrodes disposed opposite each other across adjoining grooves have opposite electrical polarity.

In addition, the resonator has a thickness t of the tuning fork tines or the tuning fork tines and the tuning fork base, and a groove thickness t1. It is needless to say that the electrodes are disposed inside the grooves and on the sides of the tuning fork tines. In this embodiment, the first electrodes 23 and 24 are disposed at the tine and the base, and also, the fourth electrodes 29 and 30 are disposed at the tine and the base. In addition, the electrodes are disposed on the sides of the tines opposite each other to the electrodes disposed inside the grooves. Namely, the electrodes are disposed opposite each other inside the grooves and on the sides of the tuning fork tines so that the electrodes disposed opposite each other are of opposite electrical polarity and the tuning fork tines are capable of vibrating in inverse phase.

Now, when a direct current (DC) voltage is applied between the electrode terminals E-E′ (E terminal: plus, E′ terminal: minus), an electric field Ex occurs in the arrow direction as shown in FIG. 2. As the electric field Ex occurs perpendicular to the electrodes disposed on the base and the tines, the electric field Ex has a very large value and a large distortion occurs at the base and the tines, so that a flexural mode, quartz crystal tuning fork resonator is obtained with a small series resistance R₁ and a high quality factor Q₁, even if it is miniaturized.

FIG. 3 shows a plan view of the resonator 10 of FIG. 1. In FIG. 3, the construction and the dimension of grooves 21, 27, 32 and 36 are described in detail. The groove 21 is constructed to include a portion of the central line 41 of the tine 20, the groove 27 is similarly constructed to include a portion of the central line 42 of the tine 26. The width W₂ of the grooves 21 and 27 (groove width W₂) which include a portion of the central lines 41 and 42 respectively, is preferable because moment of inertia of the tines 20 and 26 becomes large and the tines can vibrate in a flexural mode very easily. As a result of which the flexural mode, tuning fork, quartz crystal resonator capable of vibrating in a fundamental mode can be obtained with a small series resistance R₁ and a high quality factor Q₁.

In more detail, when part widths W₁, W₃ and groove width W₂ are taken, the tine width W of the tines 20 and 26 has a relationship of W=W₁+W₂+W₃, and a part or all of at least one of the grooves is constructed so that W₁≧W₃ or W₁<W₃. In addition, the groove width W₂ is constructed so that W₂≧W₁, W₃. In this embodiment, also, the grooves are constructed at the tuning fork tines so that a ratio(W₂/W) of the groove width W₂ and the tine width W is larger than 0.35 and less than 1, and a ratio(t₁/t) of the groove thickness t₁ and the thickness t of the tuning fork tines (tine thickness t) is less than 0.79, preferably, within a range of 0.01 to 0.79 to obtain very large moment of inertia of the tuning fork tines. That is to say, the flexural mode, quartz crystal tuning fork resonator, capable of vibrating in the fundamental mode, and having a high frequency stability can be provided with a small series resistance R₁, a high quality factor Q₁ and a small capacitance ratio r₁ because electromechanical transformation efficiency of the resonator becomes large markedly.

Likewise, length l₁ of the grooves 21 and 27 of the tines 20 and 26 extends into the base 40 in this embodiment (which has a dimension of the length 12 and the length l₃ of the grooves). Therefore, groove length and length of the tuning fork tines are given by (l₁-l₃) and (l-l₂), respectively, and a ratio of (l₁-l₃) and (l-₂) is within a range of 0.4 to 0.8 to get a flexural mode, quartz crystal tuning fork resonator with series resistance R₁ of a fundamental mode vibration smaller than series resistance R₂ of a second overtone mode vibration

Furthermore, the total length l is determined by the frequency requirement and the size of the housing case. At the same time, to get a flexural mode, quartz crystal tuning fork resonator capable of vibrating easily in a fundamental mode with suppression of the second overtone mode vibration which is unwanted mode vibration, there is a close relationship between the groove length l₁ and the total length l. Namely, a ratio(l₁/l) of the groove length l₁ and the total length l is within a range of 0.2 to 0.78 because the quantity of charges which generate within the grooves and on the sides of the tuning fork tines or the tuning fork tines and the tuning fork base can be controlled by the ratio, as a result, the second overtone mode vibration can be suppressed substantially, and simultaneously, a frequency stability of the fundamental mode vibration gets high. Therefore, the flexural mode, quartz crystal tuning fork resonator, capable of vibrating easily in the fundamental mode and having the high frequency stability can be provided.

In more detail, series resistance R₁ of the fundamental mode vibration becomes smaller than series resistance R₂ of the second overtone mode vibration. Namely, R₁<R₂, preferably, R₁<0.86R₂, therefore, a quartz crystal oscillator (oscillator circuit) comprising an amplifier (CMOS inverter), capacitors, resistors(resistance elements) and a quartz crystal unit with the quartz crystal tuning fork resonator of this embodiment can be obtained, which is capable of vibrating in the fundamental mode very easily. In addition, in this embodiment the grooves 21 and 27 of the tines 20 and 26 extend into the base 40 in series, but embodiment of the present invention includes a plurality of grooves divided into the length direction of the tuning fork tines. In addition, the grooves may be constructed only at the tuning fork tines(I₃=0), as will be shown in FIG. 4.

In this embodiment, the groove length l₁ corresponds to electrode length disposed inside the grooves, though the electrode is not shown in FIG. 3, but, when the electrode length is less than the groove length, the length l₁ is of the electrode length. Namely, the ratio(l₁/l) in this case is expressed by a ratio of electrode length l₁ of the grooves and the total length l. Also, a fork portion of this embodiment has a rectangular shape, but this invention is not limited to this, for example, the fork portion may have a U shape.

In addition, a space of between the tuning fork tines is given by W₄, and in this embodiment, the space W₄ and the groove width W₂ are constructed so that W₄≧W₂, and more, the space W₄ is within a range of 0.05 mm to 0.35 mm and the width W₂ is within a range of 0.02 mm to 0.068 mm because it is easy to form a tuning fork shape and grooves of the tuning fork tines separately by a photo-lithographic process and an etching process, as a result, a frequency stability for a fundamental mode vibration gets higher than that for a second overtone mode vibration. In this embodiment, a quartz crystal wafer with the thickness t of 0.05 mm to 0.12 mm is used. But, it is possible to use the wafer thicker than 0.12 mm.

In more detail, to obtain a flexural mode, quartz crystal tuning fork resonator with a high frequency stability which gives high time accuracy, it is necessary to obtain the resonator whose resonance frequency is not influenced by shunt capacitance because quartz crystal is a piezoelectric material and the frequency stability is very dependent on the shunt capacitance. In order to decrease the influence on the resonance frequency by the shunt capacitance, figure of merit M_(i) plays an important role. Namely, the figure of merit M_(i) that expresses inductive characteristics, electromechanical transformation efficiency and a quality factor of a flexural mode, quartz crystal tuning fork resonator, is defined by a ratio (Q_(i)/r_(i)) of a quality factor Q_(i) and capacitance ratio r_(I), namely, M_(i) is given by M_(i)=Q_(i)/r_(i), where i shows vibration order of a quartz crystal tuning fork resonator, and for example, when i=1 and 2, figures of merit M₁ and M₂ are for a fundamental mode vibration and a second overtone mode vibration, respectively.

Also, a frequency difference Δf of resonance frequency f_(s) of mechanical series independent on the shunt capacitance and resonance frequency f_(r) dependent on the shunt capacitance is inversely proportional to the figure of merit M_(i). The larger the value M_(i) becomes, the smaller the difference ΔF becomes. Namely, the influence on the resonance frequency f_(r) by the shunt capacitance decreases because it is close to the resonance frequency f_(s). Accordingly, the larger the M_(i) becomes, the higher the frequency stability of the flexural mode, quartz crystal tuning fork resonator becomes because the resonance frequency f_(r) of the resonator is almost never dependent on the shunt capacitance whose value changes with time. Namely, the flexural mode, quartz crystal tuning fork resonator can be provided with a high time accuracy.

In detail, a quartz crystal tuning fork resonator capable of vibrating in a flexural mode can be obtained with figure of merit M₁ of a fundamental mode vibration larger than figure of merit M₂ of a second overtone mode vibration by the above-described tuning fork shape, grooves and dimensions. That is to say, M₁>M₂. As an example, when resonance frequency of a quartz crystal tuning fork resonator is about 32.768 kHz for a fundamental mode vibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though there is a distribution in production, the quartz crystal tuning fork resonator has a value of M₁>65 and M₂<30, respectively.

Namely, the flexural mode, quartz crystal tuning fork resonator which is capable of vibrating in the fundamental mode can be provided with high inductive characteristics, good electromechanical transformation efficiency (small capacitance ratio r₁ and small series resistance R₁) and a high quality factor. As a result, a frequency stability of the fundamental mode vibration becomes higher than that of the second overtone mode vibration, and simultaneously, the second overtone mode vibration can be suppressed because capacitance ratio r₂ and series resistance R₂ of the second overtone mode vibration become larger than capacitance ratio r₁ and series resistance R₁ of the fundamental mode vibration, respectively.

Therefore, the resonator capable of vibrating in the fundamental mode vibration can be provided with a high time accuracy because it has the high frequency stability. Consequently, a quartz crystal oscillating circuit comprising the flexural mode, quartz crystal tuning fork resonator of this embodiment outputs a frequency of the fundamental mode vibration as an output signal, and the frequency of the output signal has a very high stability, namely, an excellent time accuracy. In other words, the quartz crystal oscillator of this embodiment has a remarkable effect such that a frequency change by ageing becomes very small. Also, a frequency of a fundamental mode vibration of the present invention is less than 200 kHz, preferably, within a range of 10 kHz to 200 kHz. Especially, 32.768 kHz is used widely.

In addition, groove length l₁ of the present invention is length of grooves constructed at tuning fork tines so that the ratio(t₁/t) of the groove thickness t₁ and the tine thickness t is less than 0.79, and the ratio(W₂/W) of the groove width W₂ and the tine width W is larger than 0.35 and less than 1, when the grooves are constructed only at the tuning fork tines, and also, when the grooves constructed at the tuning fork tines extend into a tuning fork base and at least one groove is constructed between the grooves extended into the tuning fork base, groove length l₁ of the present invention is length of grooves constructed at the tuning fork tines and the tuning fork base(groove length l₃).

Namely, when the grooves constructed at the tuning fork tines extend into the tuning fork base and at least one groove is not constructed between the grooves extended into the tuning fork base, the groove length l₁ of the present invention is length of grooves constructed at the tuning fork tines. Also, when the grooves of the tines are divided into the length direction thereof or connected via at least one step portion, the groove length l₁ is total length of the length direction satisfying the ratios(t₁/t) and (W₂/W) described above. In addition, the groove thickness t₁ of the present invention is the thinnest thickness of the grooves because quartz crystal is an anisotropic material and the groove thickness t₁ has a distribution when it is formed by a chemical etching method.

FIG. 4 shows a plan view of a flexural mode, quartz crystal tuning fork resonator 45 embodying the present invention. The resonator 45 comprises tuning fork tines 46, 47 and a tuning fork base 48. The tines 46, 47 and the base 48 are formed integrally by a chemical etching process. In this embodiment, the base 48 has cut portions 53 and 54. Also, a groove 49 is constructed to include a portion of the central line 51 of the tine 46, a groove 50 is similarly constructed to include a portion of the central line 52 of the tine 47. In this embodiment, the grooves 49 and 50 are constructed at a part of the tines 46 and 47, and have groove width W₂ and groove length l₁.

In this embodiment, though electrodes are not shown in FIG. 4, the electrodes are disposed inside the grooves 49, 50 and on sides of the tuning fork tines 46 and 47, similar to FIG. 2. In detail, the electrodes are disposed opposite each other inside the grooves and on the sides of the tuning fork tines so that the electrodes disposed opposite each other are of opposite electrical polarity and the tuning fork tines are capable of vibrating in inverse phase.

Also, in this embodiment, the width W₂ of the grooves 49 and 50 (groove width W₂) which include a portion of the central lines 51 and 52, respectively, is preferable because moment of inertia of the tines 46 and 47 becomes large and the tines are capable of vibrating in a flexural mode very easily. Also, though grooves of reverse face of the tines are not shown in FIG. 4, the grooves are constructed opposite each other to the grooves 49 and 50 at the reverse face of the tines 46 and 47, and electrodes are disposed inside the grooves and on sides of the tines, similar to FIG. 2.

In addition, the base 48 has cut portions 53 and 54, and the cut base 48 has a dimension of width W₅ (tines side) and width W₆ (opposite side to the tines side). When the base 48 is mounted at a mounting portion of a case of surface mounting type or tubular type by solder or conductive adhesives, it is necessary to satisfy W₆≧W₅ to decrease energy losses by vibration. The cut portions 53 and 54 are very effective to decrease the energy losses. Therefore, the flexural mode, quartz crystal tuning fork resonator, capable of vibrating in the fundamental mode and having the high frequency stability (high time accuracy) can be provided with a small series resistance R₁ and a high quality factor Q₁. Also, the width dimensions W=W₁+W₂+W₃ and W₄, and the length dimensions l₁, l₂ and l are as already described in relation to FIG. 3.

FIG. 5 a and FIG. 5 b are a plan view and a side view of a contour mode quartz crystal resonator capable of vibrating in a width-extensional mode embodying the present invention, so called a width-extensional mode quartz crystal resonator 62. The resonator 62 comprises vibrational portion 63, connecting portions 66, 69 and supporting portions 67, 80 including respective mounting portions 68, 81. In addition, the supporting portions 67 and 80 have respective holes 67a and 80a. Also, electrodes 64 and 65 are disposed opposite each other on upper and lower faces of the vibrational portion 63, the electrodes have opposite electrical polarities. Namely, a pair of electrodes is disposed on the vibrational portion. In this case, a fundamental mode vibration can be excited easily.

In addition, the electrode 64 extends to the mounting portion 81 through the one connecting portion 69 and the electrode 65 extends to the mounting portion 68 through the other connecting portion 66. In this embodiment, the electrodes 64 and 65 disposed on the vibrational portion 63 extend to the mounting portions of the different direction each other. However, a resonator with the same characteristics as said resonator can be obtained, even if the electrodes 64 and 65 extend to the mounting portions of the same direction each other. The resonator in this embodiment is mounted on fixing portions of a case or a lid at the mounting portions 68 and 81 by conductive adhesives or solder.

With respect to a cutting angle of the width-extensional mode quartz crystal resonator, it is shown here. First, a quartz crystal plate perpendicular to x axis, so called, X plate quartz crystal is taken. Width W₀, length L₀ and thickness T₀ which are each dimension of the X plate quartz crystal correspond to the respective directions of y, z and x axes.

Next, this X plate quartz crystal is, first, rotated with an angle θ_(x) of −25° to +25° about the x axis, and second, rotated with an angle θ_(y) of −30° to +30° about y′ axis which is the new axis of the y axis. In this case, the new axis of the x axis changes to x′ axis and the new axis of the z axis changes to z″ axis because the z axis is rotated twice about two axes the width-extensional mode quartz crystal resonator of the present invention is formed from the quartz crystal plate with the rotation angles.

In other words, according to an expression of IEEE notation, a cutting angle of the width-extensional mode quartz crystal resonator of the present invention can be expressed by XZtw(−25°-+25°)/(−30°-+30°). Also, when a turn over temperature point T_(p) is taken in a vicinity of room temperature, a cutting angle of the quartz crystal resonator may be within a range of XZt(−12°-−13.5°) or XZt(−18.5°-−19.8°) or XZtw(−13°-−18°)/±(+0.5°-+30°). Namely, said three kinds of cutting angles in this embodiment is in the same direction as the cutting angle of the DT cut quartz crystal resonator, which is formed from a rotated Y-plate about the x axis whose Y-plate is perpendicular to the y axis.

Moreover, the vibrational portion 63 has a dimension of width W₀, length L₀ and thickness Z₀, also, width W₀, length L₀ and thickness T₀ correspond to y′, z″ and x′ axes, respectively. That is, the electrodes 64 and 65 are disposed on the upper and lower faces of the vibrational portion 63 perpendicular to the x′ axis.

In addition, the vibrational portion 63 has a dimension of length L₀ greater than width W₀ and thickness T₀ smaller than the width W₀. Namely, a coupling between a width-extensional mode and a length-extensional mode gets so small as it can be ignored, as a result of which, the quartz crystal resonator can vibrate in a single width-extensional mode, and also, a width-to-length ratio (W₀/L₀) has a value smaller than 0.7 to provide the resonator with a small series resistance R₁ by increasing electrode area of the vibrational portion. In addition, a thickness-to-width ratio (T₀/W₀) has a value smaller than 0.85 to provide the resonator with a small R₁ by increasing the intensity of an electric field E_(x), These actual dimensions are, therefore, determined by the requirement characteristics for the width-extensional mode quartz crystal resonator.

In more detail, resonance frequency of the width-extensional mode quartz crystal resonator is inversely proportional to width W₀, and it is almost independent on such an other dimension as length L₀, thickness To, connecting portions and supporting potions. Also, in order to obtain a width-extensional mode quartz crystal resonator with a frequency of 4 MHz, the width W₀ is about 0.7 mm. Thus, the miniature width-extensional mode quartz crystal resonator can be provided with a frequency less than 135 MHz, preferably, within a range of 1 MHz to 135 MHz because resonance frequency of the resonator is inversely proportional to the width W₀. Also, the resonator capable of vibrating in a single width-extensional mode can be obtained from the relation of said dimensions.

Consequently, a quartz crystal oscillator comprising a quartz crystal oscillating circuit comprising the resonator of this embodiment having a high electromechanical transformation efficiency can be provided with a small series resistance R₁ and a high quality factor Q. Also, the quartz crystal oscillating circuit comprises an amplification circuit comprising an amplifier at least and a feedback circuit comprising the quartz crystal resonator and capacitors at least. In detail, the amplification circuit comprises a CMOS inverter and a feedback resistor and the feedback circuit comprises a drain resistor, the resonator, a capacitor of a gate side and a capacitor of a drain side. Therefore, an output signal of the quartz crystal oscillator of this embodiment is used as a clock signal.

Now, when an alternating current (AC) voltage is applied between the electrodes 64 and 65 shown in FIG. 5 b, an electric field E_(x) occurs alternately in the thickness direction, as shown by the arrow direction of the solid and broken lines. Consequently, the vibrational portion 63 is capable of extending and contracting in the width direction. In this embodiment, though the width-extensional mode quartz crystal resonator is described in detail, which is one of a contour mode quartz crystal resonator, this invention is not limited to this, but includes a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, each of which is capable of vibrating in a contour mode, and has a vibrational portion, connecting portions and supporting portions respectively.

Especially, for the Lame mode quartz crystal resonator, the vibrational portion and the supporting portions are connected at corners of the vibrational portion through the connecting portions and electrodes are disposed opposite each other on upper and lower faces of the vibrational portion so that the electrodes opposite each other are of opposite electrical polarity. Also, the length-extensional mode quartz crystal resonator of the present invention can be obtained by replacing the width with the length and the length with the width of the width-extensional mode quartz crystal resonator. Therefore, the connecting portions and the supporting portions are constructed in the width direction and the connecting portions are connected at ends of the vibrational portion.

FIG. 6 shows a cross-sectional view of a quartz crystal unit embodying the present invention. In this embodiment, the quartz crystal unit 170 comprises a flexural mode, quartz crystal tuning fork resonator 70, a case 71 and a lid 72. In more detail, the resonator 70 is mounted at a mounting portion 74 of the case 71 by conductive adhesives 76 or solder. Also, the case 71 and the lid 72 are connected through a connecting member 73. The resonator 70 in this embodiment is the same resonator as one of the flexural mode, quartz crystal tuning fork resonators 10 and 45 described in detail in FIG. 1-FIG. 4. Also, in this embodiment, circuit elements are connected at outside of the quartz crystal unit to get a quartz crystal oscillator. Namely, only the quartz crystal tuning fork resonator is housed in the unit (package) and also, it is housed in the unit in vacuum. In this embodiment, the quartz crystal unit of surface mounting type is shown, but the quartz crystal tuning fork resonator may be housed in a unit of tubular type. For example, when a quartz crystal tuning fork resonator is housed in the unit of tubular type, a case has two lead wires as a mounting portion and the resonator is mounted on the two lead wires. This is called a quartz crystal unit of tubular type.

In this embodiment, the quartz crystal unit comprises the flexural mode, quartz crystal tuning fork resonator, but may comprise the length-extensional mode quartz crystal resonator or the Lame mode quartz crystal resonator described above in detail, instead of the tuning fork resonator.

In addition, a member of the case and the lid is ceramics or glass and a metal or glass, respectively, and a connecting member is a metal or glass with low melting point. Also, a relationship of the resonator, the case and the lid described in this embodiment is applied to a quartz crystal oscillator of the present invention which will be described in FIG. 10

Next, a method for manufacturing a quartz crystal resonator, a quartz crystal unit and a quartz crystal oscillator of the present invention is described in detail, according to the manufacturing steps.

FIG. 7 shows an embodiment of a method for manufacturing a quartz crystal resonator, a quartz crystal unit and a quartz crystal oscillator of the present invention and a step diagram embodying the present invention. In this embodiment, a quartz crystal tuning fork resonator capable of vibrating in a flexural mode is described. The signs of S-1 to S-12 are the step numbers. First, S-1 shows a cross-sectional view of a quartz crystal wafer 140. Next, in S-2 metal film 141, for example, chromium and gold on the chromium are, respectively, disposed on upper and lower faces of the quartz crystal wafer 140 by an evaporation method or a spattering method. In addition, resist 142 is spread on said metal film 141 in S-3, and after the metal film 141 and the resist 142 were removed except those of tuning fork shape by a photo-lithographic process and an etching process, the tuning fork shape having tuning fork tines 143, 144 and a tuning fork base 145, as be shown in S-4, is integrally formed by a chemical etching process. In S-4, the resist and the metal film disposed on the tuning fork shape are removed after it was formed. When the tuning fork shape is formed, cut portions may be formed at the tuning fork base. In FIG. 7 the formation of a piece of tuning fork shape is shown, but, a plurality of individual tuning fork shapes are actually formed in a quartz crystal wafer.

Similar to the steps of S-2 and S-3, metal film and resist are spread again on the tuning fork shape of S-4 and grooves 146, 147, 148 and 149 each of which has two step difference portions along the length direction of the tuning fork tines, are formed at the tuning fork tines 143, 144 by a photo-lithographic process and an etching process, and the shape of S-5 is obtained after all of the resist and the metal film were removed. In addition, metal film and resist are spread again on the shape of S-5 and electrodes which are of opposite electrical polarity, are disposed opposite each other on sides of the tuning fork tines and inside the grooves thereof, as be shown in S-6.

Namely, electrodes 150, 153 disposed on the sides of the tuning fork tine 143 and electrodes 155, 156 disposed inside the grooves 148, 149 of the tuning fork tine 144 have the same electrical polarity. Similarly, electrodes 151, 152 disposed inside the grooves 146, 147 of the tuning fork tine 143 and electrodes 154, 157 disposed on the sides of the tuning fork tine 144 have the same electrical polarity. Two electrode terminals are, therefore, constructed. In more detail, when an alternating current (AC) voltage is applied between the terminals, the tuning fork tines are capable of vibrating in a flexural mode of inverse phase because said electrodes disposed on step difference portions of the grooves and the electrodes disposed opposite to the said electrodes have opposite electrical polarity. In the step of S-6, a piece of flexural mode, quartz crystal tuning fork resonator capable of vibrating in a fundamental mode is shown in the quartz crystal wafer, but a plurality of individual quartz crystal tuning fork resonators, each of which comprises tuning fork tines and a tuning fork base capable of vibrating in a flexural mode and has resonance frequency higher than 32.768 kHz in the fundamental mode vibration, are actually formed in the quartz crystal wafer.

Next, metal films are formed on the tuning fork tines of the individual quartz crystal tuning fork resonators in the quartz crystal wafer by a spattering method or an evaporation method so as to get the individual quartz crystal tuning fork resonators each of which has resonance frequency lower than 32.768 kHz, preferably, within a range of 29.4 kHz to 32.75 kHz.

In addition, resonance frequency for the individual resonators is adjusted by a separate step of at least twice and the first adjustment of resonance frequency for the individual resonators is performed in the quartz crystal wafer by laser trimming or a plasma etching method so that the resonance frequency of the individual resonators is within a range of 32.2 kHz to 33.08 kHz. The adjustment of frequency by laser trimming or a plasma etching method is performed by trimming the metal films disposed on the tuning fork tines to increase the resonance frequency, on the other hand, the adjustment of frequency by an evaporation method is performed by adding mass such as a metal on tuning fork tines to decrease the resonance frequency. Namely, those methods can change the resonance frequency of the resonators. Also, the individual resonators formed in the quartz crystal wafer are inspected therein and when there is a failure resonator, it is removed from the quartz crystal wafer or something is marked on it or it is remembered by a computer.

In this embodiment, the tuning fork shape is formed from the step of S-3 and after that, the grooves are formed at the tuning fork tines, namely, the tuning fork tines are formed before the grooves are formed, but this invention is not limited to said embodiment, for example, the grooves are first formed from the step of S-3 and after that, the tuning fork shape may be formed, namely, the grooves are formed before the tuning fork tines are formed. Also, the tuning fork shape and the grooves may be formed simultaneously, namely, the tuning fork tines and the grooves are formed simultaneously. In addition, the grooves each of which has two step difference portions along the direction of length of the tuning fork tines, are formed in this embodiment, but, each of the grooves may have step difference portions more than two along the length direction of the tines, at least two of which are connected via at least one step portion.

Also, in this embodiment, though the grooves are constructed at the tuning fork tines and the electrodes are disposed inside the grooves, this invention is not limited to this, namely, the grooves may not be constructed at the tuning fork tines. In more detail, the tuning fork tines have obverse and reverse faces and sides and electrodes are disposed on the obverse and reverse faces and the sides of the tines. In addition, electrodes disposed on obverse and reverse faces of tuning fork tines of the present invention implies electrodes disposed on the obverse and reverse faces of the tuning fork tines, notwithstanding there is a groove at the tines or not. Therefore, it is needless to say that this invention includes at least one connecting electrode disposed on at least one face of the obverse and reverse faces of the tines to connect two electrodes. As a result of which the tuning fork tines are capable of vibrating in inverse phase.

There are two methods of A and B in the following step, as be shown by arrow signs. For the step of A, the tuning fork base 145 of the formed flexural mode, quartz crystal tuning fork resonator 160 is first mounted on mounting portion 159 of a case 158 by conductive adhesives 161 or solder, as be shown in S-7. Next, the second adjustment of resonance frequency for the resonator 160 is performed by laser 162 or an evaporation method or a plasma etching method in S-8 so that the resonance frequency is within a range of 32.764 kHz to 32.772 kHz when the resonator is housed in a package, namely, the quartz crystal unit is provided. Finally, the case 158 and a lid 163 are connected via glass 164 with the low melting point or a metal in S-9. In this case, the connection of the case and the lid is performed in vacuum because the case 158 has no hole to close it in vacuum.

In this embodiment, though the metal films are formed on the tuning fork tines of the individual quartz crystal resonators formed in the quartz crystal wafer and resonance frequency of the individual resonators is adjusted therein by removing a part or all of the metal films by laser trimming or a plasma etching method, the present invention is not limited to this, namely, said steps may be omitted. In more detail, each of the individual resonators having resonance frequency higher than 32.768 kHz is mounted at a mounting portion of a case and after that, the resonance frequency is adjusted by an evaporation method so that it is within a range of 32.764 kHz to 32.772 kHz when a quartz crystal unit is provided.

In addition, though it is not visible in FIG. 7, the third frequency adjustment may be performed by laser trimming after the step of the connection of S-9 to get a small frequency deviation when a material of the lid is glass. As a result of which it is possible to get the resonator with the resonance frequency of 32.766 kHz to 32.77 kHz. Like this step, when the third frequency adjustment is performed, the resonance frequency of the resonators by the second frequency adjustment is adjusted so that it is within a range of 32.736 kHz to 32.8 kHz.

For the step of B, the tuning fork base 145 of the formed resonator 160 is first mounted on mounting portion 159 of a case 165 by conductive adhesives 161 or solder in S-10, in addition, in S-11 the case 165 and a lid 163 are connected by the same way as that of S-9, in more detail, after the resonator was mounted on the mounting portion of the case or after the resonator was mounted at the mounting portion and the case and the lid were connected, the second adjustment of resonance frequency is performed so that the resonance frequency is within a range of 32.764 kHz to 32.772 kHz in vacuum, but, it may be within a wider range, for example, 32.736 kHz to 32.8 kHz when the third frequency adjustment as will be shown as follows, is performed. Finally, a hole 167 constructed at the case 165 is closed in vacuum using such a metal 166 as solder or glass with the low melting point in S-12.

Also, similar to the step of A, the third adjustment of resonance frequency may be performed by laser trimming after the step of S-12 to get a small frequency deviation. As a result of which it is possible to get the resonator with the resonance frequency of 32.766 kHz to 32.77 kHz. Thus, the resonance frequency of the resonators in the case of A and B is finally within a range of 32.764 kHz to 32.772 kHz at most. Also, the second frequency adjustment may be performed after the case and the lid were connected and after that, the hole is closed in vacuum. In addition, the hole is constructed at the case, but may be constructed at the lid. Also, the frequency adjustment of the present invention is performed in vacuum or inert gas such as nitrogen gas or atmosphere, and the values described above are values in vacuum.

Therefore, the quartz crystal tuning fork resonators each of which is capable of vibrating in a flexural mode and the quartz crystal units manufactured by the above-described method are miniaturized and realized with a small series resistance R₁, a high quality factor Q₁ and low price.

Moreover, in the above-described embodiment, though the first frequency adjustment of the resonators is performed in the quartz crystal wafer and at the same time, when there is a failure resonator, something is marked on it or it is removed from the quartz crystal wafer, but the present invention is not limited to this, namely, the present invention may include the step to inspect the flexural mode, quartz crystal tuning fork resonators formed in the quartz crystal wafer therein, in other words, the step to inspect whether there is a failure resonator or not in the quartz crystal wafer. When there is the failure resonator in the wafer, it is removed from the wafer or something is marked on it or it is remembered by a computer. By including the step, it can increase a manufacturing yield of the quartz crystal resonators because it is possible to find out the failure resonator in an early step and the failure resonator does not go to the next step. As a result of which low priced flexural mode, quartz crystal tuning fork resonators can be provided with excellent electrical characteristics. In this embodiment, the frequency adjustment is performed three times by a separate step, but may be performed at least twice by a separate step. For example, the third frequency adjustment may be omitted.

In this embodiment, the frequency adjustment is performed by a separate step of at least twice. However, when a plurality of individual quartz crystal tuning fork resonators, each of which has a resonance frequency higher than 32.768 kHz, are formed in a quartz crystal wafer and each resonator is mounted at a mounting portion of a case or a lid, resonance frequency is adjusted by an evaporation method of at least once so that it is within a range of 32.764 kHz to 32.772 kHz when a quartz crystal unit is provided.

Also, for the manufacturing method of this embodiment, the steps of forming a plurality of individual quartz crystal tuning fork resonator having resonance frequency higher than 32.768 kHz by a chemical etching method and changing the resonance frequency by forming metal films on tuning fork tines of the individual resonators are not included in the frequency adjustment of the present invention.

In addition, in order to construct a quartz crystal oscillator having a quartz crystal oscillating circuit comprised of an amplification circuit having at least an amplifier and a feedback circuit having at least capacity and a quartz crystal tuning fork resonator capable of vibrating in a flexural mode, two electrode terminals of the resonators are connected electrically to the amplifier and the capacitors. Namely, the quartz crystal oscillating circuit comprises the step of connecting electrically at least the quartz crystal tuning fork resonator, the amplifier and the capacitors. More specifically, the quartz crystal oscillating circuit is constructed and connected electrically so that the amplification circuit comprises a CMOS inverter and a feedback resistor and the feedback circuit comprises the flexural mode, quartz crystal tuning fork resonator, the drain resistor, the capacitor of a gate side and the capacitor of a drain side. Also, the third frequency adjustment may be performed after the quartz crystal oscillating circuit has been constructed.

Next, an embodiment of a method for manufacturing a quartz crystal unit comprising a contour mode quartz crystal resonator such as a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, a case and a lid is described in detail, the contour mode quartz crystal resonator comprises the step of: utilizing a particle method or a chemical etching method to form a resonator comprising; a vibrational portion; connecting portions located at ends of said vibrational portion; supporting portions connected to the vibrational portion through the connecting portions; and electrodes disposed opposite each other on upper and lower faces of the vibrational portion so that the electrodes disposed opposite each other are of opposite electrical polarity.

In addition, a plurality of individual quartz crystal resonators each of which is capable of vibrating in a contour mode and a single mode, are formed in a quartz crystal wafer with resonance frequency higher than a nominal frequency, and metal films are formed on the vibrational portion in the quartz crystal wafer by a spattering method or an evaporation method so as to get the individual quartz crystal resonators each of which has resonance frequency lower than the nominal frequency.

Moreover, each of the individual quartz crystal resonators is housed in a case, and the resonance frequency of each resonator is adjusted by removing a part or all of the metal films formed on the vibrational portion by laser trimming or a plasma etching method so that a frequency deviation is within a range of −100 PPM to +100 PPM to the nominal frequency. Namely, the resonator is housed in a package with the frequency deviation.

In this embodiment, the metal films are formed on the vibrational portion, but they may not be formed on the vibrational portion. In this case, a plurality of individual contour mode quartz crystal resonators each of which is capable of vibrating in a contour mode and a single mode, are formed in a quartz crystal wafer with resonance frequency lower than a nominal frequency, and each of the individual quartz crystal resonators is housed in a case, and the resonance frequency of each resonator is adjusted by removing a part of the electrodes formed on the vibrational portion by laser trimming or a plasma etching method so that a frequency deviation is within a range of −100 PPM to +100 PPM to the nominal frequency. Namely, the resonator is housed in a package with the frequency deviation.

As described above, the contour mode quartz crystal resonators in the embodiment have such complicated shapes as comprise the vibrational portion, the connecting portions and the supporting portions. Also, the resonators in this embodiment of the present invention are generally processed by a chemical etching method, but, when the etching speed which is very dependent on a cutting angle is extremely slow, it is very difficult and impossible to process the resonators by the chemical etching method. In this case, the resonators in this embodiment of the present invention are, therefore, processed by a physical method or a mechanical method, and the resonators are formed integrally by at least one method.

Namely, particles with mass are collided with a quartz crystal plate covered by a resist corresponding to the shape of resonators by a physical or mechanical method, as a result of which the shapes of the resonators are processed because atoms or molecules of the quartz crystal plate scatter. This method is called a “particle method”. This method is substantially different from the chemical etching method and has a feature that the processing speed is also very fast.

According to the particle method, low priced quartz crystal resonators can be provided similar to the chemical etching method because the processing time of outward shapes for the resonators shorten extremely. For this particle method, a resist with elastic characteristics is used to prevent the resist from defacement by particles. As the resist, for example, a plastic resist for use in blast processing is well known. Also, for this particle method, for example, it is preferable to use particles of GC#1000 to GC#6000 or ion atoms or ion molecules as the particles for use in processing. Especially, a method by ion etching is called ” plasma etching method ” in the present invention.

Additionally, an insulation material such as S_(i)O₂ may be constructed on obverse and reverse faces of the width W₁ and the width W₃ of the tuning fork tines to prevent a short circuit of between the electrodes of the sides and the grooves thereof, and the insulation material is formed by a spattering method or an evaporation method. Also, when a tuning fork shape comprising tuning fork tines and a tuning fork base is formed by a photo-lithographic process and an etching process, cut portions may be also formed simultaneously at the tuning fork base.

Likewise, in the present embodiments the flexural mode quartz crystal resonator of tuning fork type has two tuning fork tines, but embodiments of the present invention include tuning fork tines more than two. In addition, the quartz crystal tuning fork resonators of the present embodiments are housed in a package (unit) of surface mounting type comprising a case and a lid, but may be housed in a package of tubular type.

FIG. 8 shows a diagram of an embodiment of a quartz crystal oscillating circuit constructing a quartz crystal oscillator of the present invention. In this embodiment, the quartz crystal oscillating circuit 1 comprises an amplifier (CMOS Inverter) 2, a feedback resistor 4, drain resistor 7, capacitors 5, 6 and a flexural mode, quartz crystal tuning fork resonator 3. Namely, the quartz crystal oscillating circuit 1 comprises an amplification circuit 8 having the amplifier 2 and the feedback resistor 4, and a feedback circuit 9 having the drain resistor 7, the capacitors 5, 6 and the flexural mode quartz crystal resonator 3. In addition, an output signal of the quartz crystal oscillating circuit 1 comprising the flexural mode, quartz crystal tuning fork resonator 3, capable of vibrating in a fundamental mode, is outputted through a buffer circuit (not shown in FIG. 8) from a drain side of the amplifier (CMOS Inverter).

In detail, a frequency of the fundamental mode vibration is outputted through a buffer circuit as an output signal. According to the present invention, a nominal frequency of the fundamental mode vibration is 32.768 kHz. Also, the present invention includes a divided frequency of the output signal having the frequency of 32.764 kHz to 32.772 kHz by a divided circuit. In more detail, the quartz crystal oscillator in this embodiment comprises the quartz crystal oscillating circuit and the buffer circuit, in other words, the quartz crystal oscillating circuit comprises the amplification circuit and the feedback circuit, and the amplification circuit comprises the amplifier at least and the feedback circuit comprises the flexural mode, quartz crystal tuning fork resonator and the capacitors at least. Also, the quartz crystal tuning fork resonators each of which is capable of vibrating in a flexural mode have been already described in FIG. 1-FIG. 4 in detail.

FIG. 9 shows a diagram of the feedback circuit of FIG. 8. Now, when angular frequency ω_(i) of the flexural mode, quartz crystal tuning fork resonator 3, capable of vibrating in a flexural mode, a resistance R_(d) of the drain resistor 7, capacitance C_(g), C_(d) of the capacitors 5, 6, crystal impedance R_(ei) of the quartz crystal resonator 3, an input voltage V₁, and an output voltage V₂ are taken, a feedback rate β_(i) is defined by β_(i)=|V₂|_(i)/|V₁|i, where i shows vibration order, for example, when i=1 and 2, they are for fundamental mode vibration and second overtone mode vibration, namely, when i=n, it is for n^(th) overtone mode vibration.

In addition, load capacitance C_(L) is given by C_(L)=C_(g)C_(d)/(C_(g)+C_(d)), and when C_(g)=C_(d)=C_(gd) and Rd>>R_(ei), the feedback rate β_(i) is given by β_(i)=1/(1+kC_(L) ²), where k is expressed by a function of ω_(i), R_(d) and R_(ei). Also, R_(ei) is approximately equal to series resistance R_(i).

Thus, it is easily understood from a relationship of the feedback rate β_(i) and load capacitance C_(L) that the feedback rate of resonance frequency for a fundamental mode vibration and an overtone mode vibration becomes large, respectively, according to decrease of load capacitance C_(L). Therefore, when C_(L) has a small value, an oscillation of the overtone mode occurs very easily, instead of that of the fundamental mode. This is the reason why a maximum amplitude of the overtone mode vibration becomes smaller than that of the fundamental mode vibration, and the oscillation of the overtone mode satisfies an amplitude condition and a phase condition simultaneously which are the continuous condition of an oscillation in an oscillating circuit.

In addition, in order to suppress a second overtone mode vibration and to obtain a quartz crystal oscillator comprising a quartz crystal oscillating circuit, comprising a flexural mode, quartz crystal tuning fork resonator and having an output signal of a frequency of a fundamental mode vibration, the quartz crystal oscillating circuit in this embodiment is constructed so that it satisfies a relationship of α₁/α₂>β₂/β_(i) and α₁β₁>1, where α₁ and α₂ are a amplification rate of the fundamental mode vibration and the second overtone mode vibration of an amplification circuit, and β₁ and β₂ are a feedback rate of the fundamental mode vibration and the second overtone mode vibration of a feedback circuit.

In other words, the quartz crystal oscillating circuit is constructed so that a ratio of the amplification rate α₁ of the fundamental mode vibration and the amplification rate α₂ of the second overtone mode vibration of the amplification circuit is larger than that of the feedback rate β₂ of the second overtone mode vibration and the feedback rate β₁ of the fundamental mode vibration of the feedback circuit, and a product of the amplification rate α₁ and the feedback rate β₁ of the fundamental mode vibration is larger than 1. By constructing the oscillating circuit like this, it can be provided with reduced electric current consumption and the output signal of the frequency of the fundamental mode vibration.

Also, characteristics of the amplifier of the amplification circuit constructing the quartz crystal oscillating circuit of this embodiment can be expressed by negative resistance −RL_(i). For example, when i=1, negative resistance −RL_(i) is for a fundamental mode vibration and when i=2, negative resistance −RL₂ is for a second overtone mode vibration. In this embodiment, the quartz crystal oscillating circuit is constructed so that a ratio of an absolute value of negative resistance, |−RL₁| of the fundamental mode vibration of the amplification circuit and series resistance R₁ of the fundamental mode vibration is larger than that of an absolute value of negative resistance, |−RL₂| of the second overtone mode vibration of the amplification circuit and series resistance R₂ of the second overtone mode vibration. That is to say, the oscillating circuit is constructed so that it satisfies a relationship of |−RL₁|/R₁>|−RL₂|/R₂. By constructing the oscillating circuit like this, an oscillation of the second overtone mode can be suppressed, as a result of which an output signal of a frequency of the fundamental mode vibration can be provided because an oscillation of the fundamental mode generates easily in the oscillating circuit.

FIG. 10 shows a cross-sectional view of a quartz crystal oscillator embodying the present invention. The quartz crystal oscillator 190 comprises a quartz crystal oscillating circuit, a case 91 and a lid 92. In this embodiment, circuit elements constructing the oscillating circuit are housed in a quartz crystal unit comprising a flexural mode, quartz crystal tuning fork resonator 90, the case 91 and the lid 92. Also, the quartz crystal oscillating circuit of this embodiment comprises an amplifier 98 including a feedback resistor, the quartz crystal tuning fork resonator 90, capacitors (not shown here) and a drain resistor (not shown here), and a CMOS inverter is used as the amplifier 98.

In addition, in this embodiment, the resonator 90 is mounted at a mounting portion 94 of the case 91 by conductive adhesives 96 or solder. As described above, the amplifier 98 is housed in the quartz crystal unit and mounted at the case 91. Also, the case 91 and the lid 92 are connected through a connecting member 93. The resonator 90 of this embodiment is the same as one of the flexural mode, quartz crystal tuning fork resonators 10 and 45 described in detail in FIG. 1-FIG. 4. In this embodiment, though the resonator and the amplifier are housed in the same room, the present invention is not limited to this, for example, a room of the case is divided into two rooms by a divided portion, and the amplifier is housed in one of the two rooms and the flexural mode, quartz crystal tuning fork resonator is housed in other room. Namely, the resonator and the amplifier are housed in a separate room. Therefore, the quartz crystal oscillator of the present invention also includes that construction.

Likewise, in this embodiment, a piece of flexural mode, quartz crystal tuning fork resonator is housed in the unit, but the present invention also includes a quartz crystal unit having a plurality of individual flexural mode, quartz crystal tuning fork resonators, and at least two of the plurality of individual resonators are connected electrically in parallel. In detail, the at least two resonators may be an individual resonator or may be an individual resonator that is formed integrally at each tuning base through a connecting portion.

The above-described resonators are formed by at least one method of chemical, mechanical and physical etching methods. For example, the physical etching method is a method by ion etching, so called “plasma etching”.

In addition, for the flexural mode quartz crystal tuning fork resonators of the embodiments of the present invention, the resonators are provided so that a capacitance ratio r₁ of a fundamental mode vibration gets smaller than a capacitance ratio r₂ of a second overtone mode vibration, in order to obtain a frequency change of the fundamental mode vibration larger than that of the second overtone mode vibration, versus the same change of a value of load capacitance C_(L). Namely, a variable range of a frequency of the fundamental mode vibration gets wider than that of the second overtone mode vibration. Also, C_(L) has a value less than 18 pF to decrease electric current consumption in a quartz crystal oscillating circuit.

Moreover, capacitance ratios r₁ and r₂ of a flexural mode, quartz crystal tuning fork resonator are given by r₁=C₀/C₁ and r₂=C₀/C₂, respectively, where C₀ is shunt capacitance in an electrical equivalent circuit of the resonator, and C₁ and C₂ are, respectively, motional capacitance of a fundamental mode vibration and a second overtone mode vibration in the electrical equivalent circuit of the resonator. In addition, the flexural mode, quartz crystal tuning fork resonator has a quality factor Q₁ for the fundamental mode vibration and a quality factor Q₂ for the second overtone mode vibration.

In detail, the tuning fork resonator of this embodiment is provided so that the influence on resonance frequency of the fundamental mode vibration by the shunt capacitance becomes smaller than that of the second overtone mode vibration by the shunt capacitance, namely, so that it satisfies a relationship of r₁/2Q₁ ²<r₂/2Q₂ ². As a result, the tuning fork resonator, capable of vibrating in the fundamental mode and having a high frequency stability can be provided because the influence on the resonance frequency of the fundamental mode vibration by the shunt capacitance becomes so extremely small as it can be ignored. Also, the present invention replaces r₁/2Q₁ ² with S₁ and r₂/2Q₂ ² with S₂, respectively, and here, S₁ and S₂ are called “stable factor of frequency” of the fundamental mode vibration and the second overtone mode vibration. Namely, S₁ and S₂ are given by S₁=r₁/2Q₁ ² and S₂=r₂/2Q₂ ², respectively.

In addition, when a power source is applied to the quartz crystal oscillating circuit, at least one oscillation which satisfies an amplitude condition and a phase condition of vibration starts in the circuit, and a spent time to get to about ninety percent of the steady amplitude of the vibration is called “rise time ” here. Namely, the shorter the rise time becomes, the easier the oscillation becomes. When rise time t_(r1) of the fundamental mode vibration and rise time t_(r2) of the second overtone mode vibration in the circuit are taken, t_(r1) and t_(r2) are given by t_(r1)=kQ₁/(ω₁)(−1+|−RL₁|/R₁)) and t_(r2)=kQ₂/(ω₂(−1+|−RL₂|/R₂)), respectively, where k is constant and ω₁ and ω₂ are an angular frequency for the fundamental mode vibration and the second overtone mode vibration, respectively.

From the above-described relation, it is possible to obtain the rise time t_(r1) of the fundamental mode vibration less than the rise time t_(r2) of the second overtone mode vibration. As an example, when resonance frequency of a flexural mode, quartz crystal tuning fork resonator is about 32.768 kHz for a fundamental mode vibration and the resonator has a value of W₂/W=0.5, t₁/t=0.34 and l₁/l=0.48, though there is a distribution in production, as an example, the resonator has a value of Q_(i)=62,000 and Q₂−192,000, respectively. In this embodiment, Q₂ has a value of about three times of Q₁. Accordingly, to obtain the t_(r1) less than the t_(r2), it is necessary to satisfy a relationship of |−RL₁/R₁>2|−RL₂|/R₂−1 by using a relation of ω₂=6ω₁ approximately.

Also, according to this invention, the relationship is not limited to the quartz crystal oscillating circuit comprising the resonator in this embodiment, but this invention includes all quartz crystal oscillating circuits to satisfy the relationship. By constructing the oscillating circuit like this, a quartz crystal oscillator with the flexural mode, quartz crystal tuning fork resonator can be provided with a short rise time. In other words, an output signal of the oscillator has a frequency of a fundamental mode vibration of the resonator whose frequency is within a range of 32.764 kHz to 32.772 kHz, and is outputted through a buffer circuit. Namely, the second overtone mode vibration can be suppressed in the oscillating circuit. In this embodiment, the resonator has also a value of r₁=320 and r₂=10,600 as an example.

In addition, the contour mode quartz crystal resonators described in the embodiments of the present invention, each of which is a flexural mode, quartz crystal tuning fork resonator, a width-extensional mode quartz crystal resonator, a length-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator, can be applied to an electronic apparatus comprising a display portion and a quartz crystal oscillator at least such as cellar phone, telephone, TV set, camera, video set, video camera, pagers, personal computer, printer, CD player, MD player, electronic musical instrument, car navigator, car electronics, timepiece, IC card and so forth.

In detail, the contour mode quartz crystal resonators each of which constructs a quartz crystal oscillator comprising: a quartz crystal oscillating circuit comprising; an amplification circuit and a feedback circuit as described above, are used as a clock signal of the electronic apparatus. In more detail, an output signal of the quartz crystal oscillating circuit comprising the quartz crystal tuning fork resonator capable of vibrating in a flexural mode has a frequency of 32.764 kHz to 32.772 kHz and is outputted through a buffer circuit, and the output signal is a clock signal which is used to display time at the display portion of the electronic apparatus.

Likewise, an output signal of the quartz crystal oscillating circuit comprising a width-extensional mode quartz crystal resonator or a length-extensional mode quartz crystal resonator or a Lame mode quartz crystal resonator is outputted through a buffer circuit, and the output signal is a clock signal which is used except time display of the electronic apparatus.

In the present embodiments, the metal films for frequency adjustment are formed on the tuning fork tines. As an example of the present invention, silver or gold is used as a material of the metal films and for example, the metal films are formed on at least two faces of obverse and reverse faces of the tuning fork tines. Preferably, the at least two faces are of the same faces.

As described above, it will be easily understood that the quartz crystal resonators, the quartz crystal units and the quartz crystal oscillators of the present invention may have the outstanding effects. For example, the quartz crystal oscillator comprising: the quartz crystal oscillating circuit comprising; the amplification circuit and the feedback circuit having the flexural mode, quartz crystal tuning fork resonator, capable of vibrating in a fundamental mode and having the novel shapes, the novel electrode construction and good electrical characteristics, according to the present invention may have the outstanding effects. In addition to this, while the present invention has been shown and described with reference to preferred embodiments thereof, it will be understood by those skilled in the art that the changes in shape and electrode construction can be made therein without departing from the spirit and scope of the present invention. 

1-27. (canceled)
 28. A method for manufacturing an electronic apparatus having a display portion for displaying time information and at least one quartz crystal oscillator comprised of a quartz crystal oscillating circuit having an amplification circuit and a feedback circuit, the method comprising the steps of: forming by at least one of a chemical etching method, a physical etching method, and a mechanical method a quartz crystal tuning fork resonator having a quartz crystal tuning fork base and first and second quartz crystal tuning fork tines each connected to the quartz crystal tuning fork base and having a first main surface and a second main surface opposite the first main surface, the quartz crystal tuning fork resonator having a fundamental mode of vibration and a second overtone mode of vibration each comprised of a flexural mode of an inverse phase, a series resistance R₁ of the fundamental mode of vibration and a series resistance R₂ of the second overtone mode of vibration; providing the amplification circuit having a CMOS inverter, a feedback resistor, a negative resistance −RL₁ for the fundamental mode of vibration of the quartz crystal tuning fork resonator, and a negative resistance −RL₂ for the second overtone mode of vibration thereof; providing the feedback circuit having the quartz crystal tuning fork resonator, a plurality of capacitors and a drain resistor; and electrically connecting the quartz crystal tuning fork resonator to the CMOS inverter and the feedback resistor of the amplification circuit and to the capacitors and the drain resistor of the feedback circuit; wherein a ratio |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where |−RL₁| represents an absolute value of the negative resistance for the fundamental mode of vibration of the quartz crystal tuning fork resonator and |−RL₂| represents an absolute value of the negative resistance for the second overtone mode of vibration of the quartz crystal tuning fork resonator; wherein a merit value M₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is greater than a merit value M₂ of the second overtone mode of vibration thereof, the merit values M₁ and M₂ being defined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent a quality factor of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator and r₁ and r₂ represent a capacitance ratio of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator; and wherein an output signal of the quartz crystal oscillating circuit is a clock signal for use in operation of the electronic apparatus to display time information at the display portion, the clock signal having an oscillation frequency of the fundamental mode of vibration.
 29. A method according to claim 28; wherein the forming step includes the steps of forming the quartz crystal tuning fork resonator so that the quartz crystal tuning fork resonator has a frequency of oscillation for the fundamental mode of vibration higher than 32.768 kHz and disposing a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.764 kHz to 32.772 kHz; and wherein the output signal of the quartz crystal oscillating circuit has the frequency of oscillation for the fundamental mode of vibration in the range of 32.764 kHz to 32.772 kHz.
 30. A method according to claim 29; wherein the forming step further comprises the step of forming each of the first and second quartz crystal tuning fork tines with a first side surface and a second side surface opposite the first side surface; and further comprising the steps of forming a plurality of first electrodes on the first and second main surfaces of the first and second quartz crystal tuning fork tines and a plurality of second electrodes on the first and second side surfaces of the first and second quartz crystal tuning fork tines, the first electrodes formed on the first and second main surfaces of the first quartz crystal tuning fork tine having an electrical polarity opposite to an electrical polarity of the first electrodes formed on the first and second main surfaces of the second quartz crystal tuning fork tine, and the second electrodes formed on the first and second side surfaces of the first quartz crystal tuning fork tine having an electrical polarity opposite to an electrical polarity of the second electrodes formed on the first and second side surfaces of the second quartz crystal tuning fork tine; wherein the series resistance R₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R₂ of the second overtone mode of vibration thereof; and wherein the capacitance ratio r₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the capacitance ratio r₂ of the second overtone mode of vibration thereof.
 31. A method according to claim 30; further comprising the steps of providing a case having an open end; providing a lid for covering the open end of the case; mounting the quartz crystal tuning fork resonator on a mounting portion of the case, and connecting the lid to the case to cover the open end thereof; and further comprising the step of providing a surface mounting-type quartz crystal unit having the quartz crystal tuning fork resonator, the case and the lid.
 32. A method according to claim 30; further comprising the steps of providing a case having two lead wires and an open end; providing a lid for covering the open end of the case; mounting the quartz crystal tuning fork resonator on the two lead wires of the case, and covering the open end of the case by the lid; and further comprising the step of providing a tubular-type quartz crystal unit having the quartz crystal tuning fork resonator, the case having two lead wires, and the lid.
 33. A method according to claim 30; further comprising the steps of connecting the first electrodes formed on the first and second main surfaces of the first quartz crystal tuning fork to the second electrodes formed on the first and second side surfaces of the second quartz crystal tuning fork tine so that the first electrodes of the first quartz crystal tuning fork tine and the second electrodes of the second quartz crystal tuning fork tine define a first electrode terminal; and connecting the second electrodes formed on the first and second side surfaces of the first quartz crystal tuning fork tine to the first electrodes on the first and second main surfaces of the second quartz crystal tuning fork tine so that the second electrodes of the first quartz crystal tuning fork tine and the first electrodes of the second quartz crystal tuning fork tine define a second electrode terminal.
 34. A method according to claim 33; wherein the merit value M₂ for the second overtone mode of vibration of the quartz crystal tuning fork resonator is less than 30 so that the second overtone mode of vibration thereof is suppressed; and wherein when a stable factor S₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator and a stable factor S2 of the second overtone mode of vibration thereof are defined by r₁/2Q₁ ² and r₂/2Q₂ ², respectively, S₁ is less than S₂.
 35. A method according to claim 28; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines; and further comprising the step of adjusting in a plurality of different steps a frequency of oscillation of the quartz crystal tuning fork resonator.
 36. A method according to claim 35; wherein the forming step includes the steps of forming the quartz crystal tuning fork resonator having a frequency of oscillation for the fundamental mode of vibration higher than 32.768 kHz and disposing a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprises the steps of adjusting the frequency of oscillation for the fundamental mode of vibration to a first preselected frequency of oscillation and adjusting the frequency of oscillation for the fundamental mode of vibration to a second preselected frequency of oscillation by trimming at least one of the metal films disposed on at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator.
 37. A method according to claim 36; wherein the first preselected frequency of oscillation is in the range of 32.2 kHz to 33.08 kHz; and wherein the second preselected frequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.
 38. A method according to claim 37; wherein the output signal of the quartz crystal oscillating circuit comprising the quartz crystal tuning fork resonator has the frequency of oscillation for the fundamental mode of vibration in the range of 32.764 kHz to 32.772 kHz.
 39. A method according to claim 37; further comprising the step of providing a surface mounting-type quartz crystal unit having the quartz crystal tuning fork resonator, a case and a lid.
 40. A method according to claim 37; further comprising the steps of providing a tubular-type quartz crystal unit having the quartz crystal tuning fork resonator, a case having two lead wires, and a lid, and mounting the quartz crystal tuning fork resonator on the two lead wires of the case.
 41. A method according to claim 37; wherein each of the first and second quartz crystal tuning fork tines has a first side surfaces and a second side surface opposite the first side surface; wherein the forming step comprises the step of disposing electrodes on the first and second side surfaces of the first and second quartz crystal tuning fork tines so that the electrodes disposed on the first and second side surfaces of the first quartz crystal tuning fork tine have an electrical polarity opposite to an electrical polarity of the electrodes disposed on the first and second side surfaces of the second quartz crystal tuning fork tine; wherein the series resistance R₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R₂ of the second overtone mode of vibration thereof; and wherein the capacitance ratio r₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the capacitance ratio r₂ of the second overtone mode of vibration thereof.
 42. A method according to claim 41; wherein a spaced-apart distance between the first and second quartz crystal tuning fork tines is within a range of 0.05 mm to 0.35 mm.
 43. A method according to claim 35; wherein the forming step further comprises the step of forming at least one groove having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines.
 44. A method according to claim 43; wherein the at least one groove has a width within a range of 0.02 mm to 0.068 mm.
 45. A method according to claim 43; wherein a length of the at least one groove is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 46. A method according to claim 43; wherein a spaced-apart distance between the first and second quartz crystal tuning fork tines is within a range of 0.05 mm to 0.35 mm and is greater than or equal to a width of the at least one groove.
 47. A method according to claim 46; wherein the forming step includes the step of forming the first and second quartz crystal tuning fork tines simultaneously with the at least one groove.
 48. A method according to claim 43; wherein the step of forming the at least one groove having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that a width of at least one of the grooves formed in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than a distance in the width direction of the at least one groove measured from an outer edge of the at least one groove to an outer edge of the corresponding one of the first and second quartz crystal tuning fork tines.
 49. A method according to claim 48; wherein the forming step comprises the step of forming the first and second quartz crystal tuning fork tines in a step different from and before a step of forming the at least one groove.
 50. A method according to claim 48; wherein the forming step comprises the step of forming the first and second quartz crystal tuning fork tines in a step different from and after a step of forming the at least one groove.
 51. A method according to claim 48; wherein each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a central linear portion; wherein the at least one groove formed in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed in the central linear portion of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a length of at least one of the grooves formed in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 52. A method according to claim 48; wherein each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a central linear portion; wherein the at least one groove formed in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed in the central linear portion of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a spaced-apart distance between the first and second quartz crystal tuning fork tines is greater than or equal to a width of the at least one groove.
 53. A method according to claim 43; wherein the step of forming the at least one groove having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines, a width of the at least one groove being defined by W₂, a distance in the width direction of the at least one groove measured from a first outer edge of the at least one groove to a first outer edge of the corresponding one of the first and second quartz crystal tuning fork tines being defined by W₁, and a distance in the width direction of the at least one groove measured from a second outer edge opposite to the first outer edge of the at least one groove to a second outer edge opposite to the first outer edge of the corresponding one of the first and second quartz crystal tuning fork tines being defined by W₃; and wherein W₁ is greater than or equal to W₃.
 54. A method according to claim 43; wherein the step of forming the at least one groove having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines, a width of the at least one groove being defined by W₂, a distance in the width direction of the at least one groove measured from a first outer edge of the at least one groove to a first outer edge of the corresponding one of the first and second quartz crystal tuning fork tines being defined by W₁, and a distance in the width direction of the at least one groove measured from a second outer edge opposite to the first outer edge of the at least one groove to a second outer edge opposite to the first outer edge of the corresponding one of the first and second quartz crystal tuning fork tines being defined by W₃; and wherein W₁ is less than W₃ .
 55. A method according to claim 43; wherein the step of forming the at least one groove in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines, each of the grooves having a first outer edge and a second outer edge opposite to the first outer edge in the width direction of the corresponding one of the first and second quartz crystal tuning fork tines; wherein each of the first and second quartz crystal tuning fork tines has a first outer edge and a second outer edge opposite to the first outer edge; wherein a first part of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed between the first outer edge of the corresponding at least one groove and the first outer edge of the corresponding one of the first and second quartz crystal tuning fork tines; wherein a second part of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed between the second outer edge of the corresponding at least one groove and the second outer edge of the corresponding one of the first and second quartz crystal tuning fork tines; and wherein an insulation material is disposed on each of at least two of the first and second parts of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines.
 56. A method according to claim 55; wherein the insulation material comprises S_(i)O₂.
 57. A method according to claim 43; wherein the quartz crystal tuning fork base has a first side surface connected to the first and second quartz crystal tuning fork tines, a second side surface opposite the first side surface, a third side surface having a cut portion, and a fourth side surface opposite the third side surface and having a cut portion, a width W₅ of the quartz crystal tuning fork base being disposed between the first side surface and each of at least two of the cut portions of the third and fourth side surfaces, and a width W₆ of the quartz crystal tuning fork base being disposed between the second side surface and each of at least two of the cut portions of the third and fourth side surfaces; and wherein W₅ is less than or equal to W₆.
 58. A method according to claim 43; wherein the step of forming the at least one groove in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a spaced-apart distance between the first and second quartz crystal tuning fork tines is within a range of 0.05 mm to 0.35 mm and greater than or equal to a width of the at least one groove.
 59. A method according to claim 43; wherein the step of forming the at least one groove in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming a plurality of grooves having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein at least two of the grooves are divided in a lengthwise direction of the corresponding one of the first and second quartz crystal tuning fork tines.
 60. A method according to claim 59; wherein each of the first and second quartz crystal tuning fork tines has a first side surface and a second side surface opposite the first side surface; wherein the forming step further comprises the step of forming a first electrode on each of the first and second side surfaces of the first and second quartz crystal tuning fork tines and forming a second electrode having an electrical polarity opposite to an electrical polarity of the first electrode on each of at least four of the stepped portions of at least two of the grooves in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein an overall length of at least two of the grooves each having the second electrode opposite the first electrode is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 61. A method according to claim 35; further comprising the steps of providing a case having a mounting portion and an open end, providing a lid for covering the open end of the case, mounting the quartz crystal tuning fork resonator on the mounting portion of the case and connecting the lid to the case to cover the open end thereof; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines so that the frequency of oscillation for the fundamental mode of vibration of the quartz crystal tuning fork resonator is higher than 32.768 kHz, and forming a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprises the steps of adjusting in the quartz crystal wafer the frequency of oscillation for the fundamental mode of vibration of the quartz crystal tuning fork resonator by trimming at least one of the metal films disposed on at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.2 kHz to 33.08 kHz and adjusting the frequency of oscillation for the fundamental mode of vibration thereof after the mounting step or after the mounting and connecting steps so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.764 kHz to 32.772 kHz.
 62. A method according to claim 61; further comprising the step of providing a surface mounting-type quartz crystal unit having the quartz crystal tuning fork resonator, a case and a lid.
 63. A method according to claim 61; further comprising the steps of providing a tubular-type quartz crystal unit having the quartz crystal tuning fork resonator, a case having two lead wires, and a lid, and mounting the quartz crystal tuning fork resonator on the two lead wires of the case.
 64. A method according to claim 28; wherein the at least one quartz crystal oscillator comprised of a quartz crystal oscillating circuit comprises first and second quartz crystal oscillators, a mode of vibration of a quartz crystal resonator of the first quartz crystal oscillator being different from that of a quartz crystal resonator of the second quartz crystal oscillator; and wherein the quartz crystal resonator of one of the first and second quartz crystal oscillators comprises one of a length-extensional mode quartz crystal resonator, a width-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator.
 65. A method for manufacturing an electronic apparatus having a display portion for displaying time information and at least one quartz crystal oscillator comprised of a quartz crystal oscillating circuit having an amplification circuit and a feedback circuit, the method comprising the steps of: forming by at least one of a chemical etching method, a physical etching method, and a mechanical method a quartz crystal tuning fork resonator having a quartz crystal tuning fork base and first and second quartz crystal tuning fork tines each connected to the quartz crystal tuning fork base and having a first main surface and a second main surface opposite the first main surface, the quartz crystal tuning fork resonator having a fundamental mode of vibration and a second overtone mode of vibration each comprised of a flexural mode of an inverse phase, a series resistance R₁ of the fundamental mode of vibration, a series resistance R₂ of the second overtone mode of vibration, and at least one groove having a plurality of stepped portions formed in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; providing the amplification circuit having a CMOS inverter, a feedback resistor, a negative resistance −RL₁ for the fundamental mode of vibration of the quartz crystal tuning fork resonator, and a negative resistance −RL₂ for the second overtone mode of vibration thereof; providing the feedback circuit having the quartz crystal tuning fork resonator, a plurality of capacitors and a drain resistor; and electrically connecting the quartz crystal tuning fork resonator to the CMOS inverter and the feedback resistor of the amplification circuit and to the capacitors and the drain resistor of the feedback circuit; wherein a ratio |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where |−RL₁| represents an absolute value of the negative resistance of the fundamental mode of vibration of the amplification circuit and |−RL₂| represents an absolute value of the negative resistance of the second overtone mode of vibration of the amplification circuit; wherein a merit value M₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is greater than a merit value M₂ of the second overtone mode of vibration thereof, the merit values M₁ and M₂ being defined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent a quality factor of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator and r₁ and r₂ represent a capacitance ratio of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator; and wherein an output signal of the quartz crystal oscillating circuit is a clock signal for use in operation of the electronic apparatus to display time information at the display portion, the clock signal having an oscillation frequency of the fundamental mode of vibration.
 66. A method according to claim 65; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines; and further comprising the step of adjusting in a plurality of different steps a frequency of oscillation of the quartz crystal tuning fork resonator.
 67. A method according to claim 66; wherein the forming step includes the steps of forming the quartz crystal tuning fork resonator having a frequency of oscillation for the fundamental mode of vibration higher than 32.768 kHz and disposing a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprises the steps of adjusting the frequency of oscillation for the fundamental mode of vibration to a first preselected frequency of oscillation and adjusting the frequency of oscillation for the fundamental mode of vibration to a second preselected frequency of oscillation by trimming at least one of the metal films disposed on the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator.
 68. A method according to claim 67; wherein the first preselected frequency of oscillation is in the range of 32.2 kHz to 33.08 kHz; and wherein the second preselected frequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.
 69. A method according to claim 68; wherein the step of forming the at least one groove having a plurality of stepped portions in at least one of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines comprises the step of forming the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines so that a width of at least one of the grooves formed in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is greater than a distance in the width direction of the at least one groove measured from an outer edge of the at least one groove to an outer edge of the corresponding one of the first and second quartz crystal tuning fork tines.
 70. A method according to claim 69; wherein each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a central linear portion; wherein the at least one groove formed in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed in the central linear portion of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a length of at least one of the grooves formed in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 71. A method according to claim 69; wherein each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a central linear portion; wherein the at least one groove formed in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed in the central linear portion of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a spaced-apart distance between the first and second quartz crystal tuning fork tines is greater than or equal to a width of the at least one groove.
 72. A method according to claim 69; wherein a width W₂ of at least one of the grooves formed in the first and second main surfaces of each of the quartz crystal tuning fork tines is within a range of 0.03 mm to 0.12 mm; wherein a ratio W₂/W is greater than 0.35 and less than 1, where W represents a width of each of the quartz crystal tuning fork tines; and wherein a length of at least one groove having the width within a range of 0.03 mm to 0.12 mm and the ratio greater than 0.35 and less than 1 is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 73. A method according to claim 69; wherein each of the first and second quartz crystal tuning fork tines has a first side surface and a second side surface opposite the first side surface; wherein at least one of the grooves formed in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a first stepped portion and a second stepped portion, the first stepped portion being opposite the first side surface and the second stepped portion being opposite the second side surface; wherein a first electrode is disposed on each of the first and second stepped portions and a second electrode is disposed on each of the first and second side surfaces of each of the first and second quartz crystal tuning fork tines so that the first electrode is disposed opposite the second electrode and has an electrical polarity opposite to an electrical polarity of the second electrode; and wherein a length of at least one groove having the first and second stepped portions on which the first electrode is disposed opposite the second electrode is within a range of 40% to 80% of a length of each of the first and second quartz crystal tuning fork tines.
 74. A method according to claim 69; wherein a ratio W₂/W is greater than 0.35 and less than 1, where W₂ represents a width of at least one of the grooves formed in the first and second main surfaces of each of the quartz crystal tuning fork tines and W represents a width of each of the quartz crystal tuning fork tines; and wherein the at least one groove has a width within a range of 0.02 mm to 0.068 mm.
 75. A method according to claim 69; wherein each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a central linear portion; wherein the at least one groove formed in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines is formed in the central linear portion of each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein each of the first and second quartz crystal tuning fork tines has side surfaces comprising an inner side surface and an outer side surface opposite the inner side surface; and further comprising a plurality of first electrodes disposed in the grooves of the first and second quartz crystal tuning fork tines and a plurality of second electrodes disposed on the inner and outer side surfaces of the first and second quartz crystal tuning fork tines, the second electrodes of each of the first and second quartz crystal tuning fork tines having an electrical polarity opposite to an electrical polarity of the first electrodes of each of the first and second quartz crystal tuning fork tines.
 76. A method according to claim 75; wherein the first electrodes disposed in the grooves of the first quartz crystal tuning fork tine are connected to the second electrodes disposed on the inner and outer side surfaces of the second quartz crystal tuning fork tine so that the first electrodes of the first quartz crystal tuning fork tine and the second electrodes of the second quartz crystal tuning fork tine define a first electrode terminal; and wherein the second electrodes disposed on the inner and outer side surfaces of the first quartz crystal tuning fork tine are connected to the first electrodes disposed in the grooves of the second quartz crystal tuning fork tine so that the second electrodes of the first quartz crystal tuning fork tine and the first electrodes of the second quartz crystal tuning fork tine define a second electrode terminal.
 77. A method according to claim 76; wherein the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a first stepped portion and a second stepped portion opposite the first stepped portion, the first stepped portion being opposite the inner side surface of each of the first and second quartz crystal tuning fork tines and the second stepped portion being opposite the outer side surface of each of the first and second quartz crystal tuning fork tines, the inner side surface of the first quartz crystal tuning fork tine confronting the inner side surface of the second quartz crystal tuning fork tine; and wherein the first electrodes are disposed on the first and second stepped portions of the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines.
 78. A method according to claim 77; wherein when a direct current voltage is applied between the first and second electrode terminals, a direction of an x-axis element of an inner electric field generated between the second electrode disposed on the inner side surface of the first quartz crystal tuning fork tine and the first electrode disposed on the first stepped portion of the first quartz crystal tuning fork tine is the same as a direction of an x-axis element of an inner electric field generated between the second electrode disposed on the inner side surface of the second quartz crystal tuning fork tine and the first electrode disposed on the first stepped portion of the second quartz crystal tuning fork tine; wherein a direction of an x-axis element of an outer electric field generated between the second electrode disposed on the outer side surface of the first quartz crystal tuning fork tine and the first electrode disposed on the second stepped portion of the first quartz crystal tuning fork tine is the same as a direction of an x-axis element of an outer electric field generated between the second electrode disposed on the outer side surface of the second quartz crystal tuning fork tine and the first electrode disposed on the second stepped portion of the second quartz crystal tuning fork tine; and wherein the direction of the x-axis element of each of at least two of the inner electric fields of the first and second quartz crystal tuning fork tines is of the direct opposite to that of the x-axis element of each of at least two of the outer electric fields of the first and second quartz crystal tuning fork tines.
 79. A method according to claim 78; wherein the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines has a base portion, the base portion of the at least one groove in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines being disposed opposite each other in a thickness direction of the first and second quartz crystal tuning fork tines; wherein the first electrodes are disposed on the base portions of the grooves in the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and wherein a direct current voltage is applied between the first and second electrode terminals, no electric field is generated between the first electrodes disposed in the opposite base portions of the first and second quartz crystal tuning fork tines.
 80. A method according to claim 65; wherein the forming step includes the steps of forming the quartz crystal tuning fork resonator having a frequency of oscillation for the fundamental mode of vibration higher than 32.768 kHz, and forming a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 29.4 kHz to 32.75 kHz; and further comprising the step of adjusting the frequency of oscillation for the fundamental mode of vibration of the quartz crystal tuning fork resonator by trimming at least one of the metal films disposed on the first and second main surfaces of the first and second quartz crystal tuning fork tines so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.764 kHz to 32.772 kHz.
 81. A method according to claim 66; further comprising the steps of providing a case having a mounting portion and an open end, providing a lid for covering the open end of the case, mounting the quartz crystal tuning fork resonator on the mounting portion of the case and connecting the lid to the case to cover the open end thereof; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines so that the frequency of oscillation for the fundamental mode of vibration of the quartz crystal tuning fork resonator is higher than 32.768 kHz, and forming a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation for the fundamental mode of vibration is in the range of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprises the steps of adjusting in the quartz crystal wafer the frequency of oscillation for the fundamental mode of vibration of the quartz crystal tuning fork resonator by trimming at least one of the metal films disposed on the first and second main surfaces of the first and second quartz crystal tuning fork tines so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.2 kHz to 33.08 kHz and adjusting the frequency of oscillation for the fundamental mode of vibration thereof after the mounting step or after the mounting and connecting steps so that the frequency of oscillation for the fundamental mode of vibration is in the range of 32.764 kHz to 32.772 kHz.
 82. A method for manufacturing an electronic apparatus having a display portion for displaying time information and first and second quartz crystal oscillators comprised of first and second quartz crystal oscillating circuits each having a quartz crystal resonator, an amplifier, a plurality of resistors, and a plurality of capacitors, a mode of vibration of the quartz crystal resonator of the first quartz crystal oscillating circuit being different from that of the quartz crystal resonator of the second quartz crystal oscillating circuit, the quartz crystal resonator of one of the first and second quartz crystal oscillating circuits comprising a quartz crystal tuning fork resonator capable of vibrating in a flexural mode of an inverse phase and having a fundamental mode of vibration and a second overtone mode of vibration, the method comprising the steps of: forming by at least one of a chemical etching method, a physical etching method, and a mechanical method the quartz crystal tuning fork resonator having a quartz crystal tuning fork base and first and second quartz crystal tuning fork tines each connected to the quartz crystal tuning fork base and having a first main surface and a second main surface opposite the first main surface, a series resistance R₁ of the fundamental mode of vibration and a series resistance R₂ of the second overtone mode of vibration; providing an amplification circuit having a CMOS inverter, a feedback resistor, a negative resistance −RL₁ of a fundamental mode of vibration thereof, and a negative resistance −RL₂ of a second overtone mode of vibration thereof; providing a feedback circuit having the quartz crystal tuning fork resonator, a plurality of capacitors and a drain resistor; and electrically connecting the quartz crystal tuning fork resonator to the CMOS inverter and the feedback resistor of the amplification circuit and to the capacitors and the drain resistor of the feedback circuit; wherein a ratio |−RL₁|/R₁ is greater than 2|−RL₂|/R₂−1, where |−RL₁| represents an absolute value of the negative resistance of the fundamental mode of vibration of the amplification circuit and |−RL₂| represents an absolute value of the negative resistance of the second overtone mode of vibration of the amplification circuit; wherein a merit value M₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is greater than a merit value M₂ of the second overtone mode of vibration thereof, the merit values M₁ and M₂ being defined by the ratios Q₁/r₁ and Q₂/r₂, respectively, where Q₁ and Q₂ represent a quality factor of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator and r₁ and r₂ represent a capacitance ratio of the fundamental mode of vibration and the second overtone mode of vibration, respectively, of the quartz crystal tuning fork resonator; and wherein an output signal of the quartz crystal oscillating circuit comprising the quartz crystal tuning fork resonator is a clock signal for use in operation of the electronic apparatus to display time information at the display portion, the clock signal having an oscillation frequency of the fundamental mode of vibration.
 83. A method according to claim 82; wherein the series resistance R₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the series resistance R₂ of the second overtone mode of vibration thereof; and wherein the capacitance ratio r₁ of the fundamental mode of vibration of the quartz crystal tuning fork resonator is less than the capacitance ratio r₂ of the second overtone mode of vibration thereof.
 84. A method according to claim 83; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines; and further comprising the step of adjusting in a plurality of different steps a frequency of oscillation of the quartz crystal tuning fork resonator; wherein the forming step includes the steps of forming the quartz crystal tuning fork resonator having a frequency of oscillation higher than 32.768 kHz, and forming a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation is in the range of 29.4 kHz to 32.75 kHz; and further comprising the step of adjusting the frequency of oscillation of the quartz crystal tuning fork resonator by trimming at least one of the metal films disposed on the first and second main surfaces of the first and second quartz crystal tuning fork tines so that the frequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.
 85. A method according to claim 83; wherein the forming step further comprises the step of forming at least one groove having a plurality of stepped portions in each of the first and second main surfaces of each of the first and second quartz crystal tuning fork tines; and further comprising the steps of providing a case having a mounting portion and an open end, providing a lid for covering the open end of the case, mounting the quartz crystal tuning fork resonator on the mounting portion of the case and connecting the lid to the case to cover the open end thereof; wherein the forming step includes the step of etching a quartz crystal wafer to form the quartz crystal tuning fork base and the first and second quartz crystal tuning fork tines so that the frequency of oscillation of the quartz crystal tuning fork resonator is higher than 32.768 kHz, and forming a metal film on each of at least two of the first and second main surfaces of the first and second quartz crystal tuning fork tines of the quartz crystal tuning fork resonator by a spattering method or an evaporation method so that the frequency of oscillation is in the range of 29.4 kHz to 32.75 kHz; and wherein the adjusting step comprises the steps of adjusting in the quartz crystal wafer the frequency of oscillation of the quartz crystal tuning fork resonator by trimming at least one of the metal films disposed on the first and second main surfaces of the first and second quartz crystal tuning fork tines so that the frequency of oscillation is in the range of 32.2 kHz to 33.08 kHz and adjusting the frequency of oscillation thereof after the mounting step or after the mounting and connecting steps so that the frequency of oscillation is in the range of 32.764 kHz to 32.772 kHz.
 86. A method according to claim 82; wherein the quartz crystal resonator of one of the first and second quartz crystal oscillators comprises one of a length-extensional mode quartz crystal resonator, a width-extensional mode quartz crystal resonator and a Lame mode quartz crystal resonator. 